### Explicit Estimate on Primes Between Consecutive Cubes

Yuan-You Fu-Rui Cheng
Source: Rocky Mountain J. Math. Volume 40, Number 1 (2010), 117-153.
First Page:
Primary Subjects: 11Y35, 11N05
We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber.

Permanent link to this document: http://projecteuclid.org/euclid.rmjm/1268655519
Digital Object Identifier: doi:10.1216/RMJ-2010-40-1-117
Zentralblatt MATH identifier: 05704108
Mathematical Reviews number (MathSciNet): MR2607111

### References

L.V. Ahlfors, Complex analysis, 2nd ed., McGraw-Hill Book Company, New York, 1979.
Mathematical Reviews (MathSciNet): MR510197
R.C. Baker and G. Harman, The difference between consecutive primes, Proc. London Math. Soc. 2 (1996), 261.
Mathematical Reviews (MathSciNet): MR1367079
Digital Object Identifier: doi:10.1112/plms/s3-72.2.261
C. Caldwell and Y. (Fred) Cheng, Determining Mills' constants and a note on Honaker's problem J. Integer Sequences 8 (2005), 1-9.
K. Chandrasekharan, Arithmetical functions, Springer-Verlag, New York, 1970.
Mathematical Reviews (MathSciNet): MR277490
Y. (Fred) Cheng, Explicit estimates involving divisor functions, J. Number Theory, submitted.
Y. (Fred) Cheng and Sidney W. Graham, Explicit estimates for the Riemann zeta function, Rocky Mountain J. Math. 34 (2004), 1261-1290.
Mathematical Reviews (MathSciNet): MR2095256
Digital Object Identifier: doi:10.1216/rmjm/1181069799
Project Euclid: euclid.rmjm/1181069799
Y. (Fred) Cheng and Barnet Weinstock, Explicit estimates on prime numbers, Rocky Mountain J. Math., accepted.
H. Davenport, Multiplicative number theory, Springer-Verlag, New York, 1980.
Mathematical Reviews (MathSciNet): MR606931
H.M. Edwards, Riemann's zeta-function, Academic Press, New York, 1974.
Mathematical Reviews (MathSciNet): MR466039
K. Ford, Zero-free regions for the Riemann zeta-function, Proc. Millenial Conference on Number Theory, Urbana, IL, 2000.
D.A. Goldston and S.M. Gonek, A note on the number of primes in short intervals, Proc. Amer. Math. Soc. 3 (1990), 613-620.
Mathematical Reviews (MathSciNet): MR1002158
Zentralblatt MATH: 0698.10026
Digital Object Identifier: doi:10.2307/2047778
G.H. Hardy and E.M. Wright, An introduction to the theory of numbers, 5th ed., Clarendon Press, Oxford, 1979.
Mathematical Reviews (MathSciNet): MR568909
G. Hoheisel, Primzahlprobleme in der Analysis, Sitz. Preuss. Akad. Wiss. 33 (1930), 580-588.
M.N. Huxley, The distribution of prime numbers, Oxford University Press, Oxford, 1972.
Mathematical Reviews (MathSciNet): MR444593
Zentralblatt MATH: 0248.10030
A.E. Ingham, On the estimation of $N(\sigma, T)$, Quart. J. Math. 11 (1940), 291-292.
Mathematical Reviews (MathSciNet): MR3649
Digital Object Identifier: doi:10.1093/qmath/os-11.1.201
K. Ireland and M. Rosen, A classical introduction to modern number theory, 2nd ed., Springer-Verlag, New York, 1990.
Mathematical Reviews (MathSciNet): MR1070716
A. Ivić, The Riemann zeta function, John Wiley & Sons, New York, 1985.
Mathematical Reviews (MathSciNet): MR792089
H. Iwaniec and J. Pintz, Primes in short intervals, Monat. Math. 98 (1984), 115-143.
Mathematical Reviews (MathSciNet): MR776350
L. Kaniecki, On differences of primes in short intervals under the Riemann hypothesis, Demonstrat. Math 1 (1998), 121-124.
Mathematical Reviews (MathSciNet): MR1623811
Zentralblatt MATH: 0916.11050
F. Kevin, A new result on the upper bound for the Riemann zeta function, preprint, 2001.
H.L. Montgomery, Zeros of $L$-functions, Invent. Math. 8 (1969), 346-354.
Mathematical Reviews (MathSciNet): MR249375
Zentralblatt MATH: 0204.37401
Digital Object Identifier: doi:10.1007/BF01404638
J.B. Rosser, Explicit bounds for some functions of prime numbers, Amer. J. Math. 63 (1941), 211-232.
Mathematical Reviews (MathSciNet): MR3018
Digital Object Identifier: doi:10.2307/2371291
J.B. Rosser and L. Schoenfeld, Approximate formulas for some functions of prime numbers, Illinois J. Math. 6 (1962), 64-94.
Mathematical Reviews (MathSciNet): MR137689
Zentralblatt MATH: 0122.05001
Project Euclid: euclid.ijm/1255631807
--------, Sharper bounds for Chebyshev functions $\theta(x)$ and $\psi(x)$ I, Math. Comp. 29 (1975), 243-269.
Mathematical Reviews (MathSciNet): MR457373
Zentralblatt MATH: 0295.10036
Digital Object Identifier: doi:10.2307/2005479
L. Schoenfeld, Sharper bounds for Chebyshev functions $\theta(x)$ and $\psi(x)$ II, Math. Comp. 30 (1976), 337-360.
Mathematical Reviews (MathSciNet): MR457374
Digital Object Identifier: doi:10.2307/2005976
Titchmarsh, The theory of the Riemann zeta function, Oxford Science Publications, 1986.
J. Van de Lune, H.J.J. te Diele and D.T. Winter, On the zeros of the Riemann zeta function in the critical strip, IV, Math. Comp. 47 (1986), 67-681.
Mathematical Reviews (MathSciNet): MR829646
C.Y. Yildirim, A survey of results on primes in short intervals, in Number theory and its applications, %(Ankara, 1996), Lecture Notes in Pure and Appl. Math. 204 Dekker, New York, 1999.
Mathematical Reviews (MathSciNet): MR1661672
D. Zinoviev, On Vinogradov's constant in Goldbach's ternary problem, J. Number Theory 65 (1997), 334-358.
Mathematical Reviews (MathSciNet): MR1462848
Zentralblatt MATH: 0876.11047
Digital Object Identifier: doi:10.1006/jnth.1997.2141